Feature Automata and Recognizable Sets of Feature Trees

Feature trees generalize first-order trees whereby argument positions become keywords (features) from an infinite symbol set . Constructor symbols can occur with any argument positions, in any finite number. Feature trees are used to model flexible records; the assumption on the infiniteness of accounts for dynamic record field updates.
We develop a universal algebra framework for feature trees. We introduce the classical set-defining notions: automata, regular expressions and equational systems, and show that they coincide. This extension of the regular theory of trees requires new notions and proofs. Roughly, a feature automaton reads a feature tree in two directions: along its branches and along the fan-out of each node.
We illustrate the practical motivation of our regular theory of feature trees by pointing out an application on the programming language LIFE.